The MMV-form sparsity-inducing norms for the channel \(\mathbf {H}\)  and the failure deviation \(\mathbf {D}\)  are introduced as follows.
The MMV-form atomic norm is defined as [1]}
\(\Vert \mathbf {H} \Vert _{\mathcal {A}_\mathrm {MMV}} = \inf \left\lbrace  \sum _{l} |\alpha _l| \bigg | \mathbf {H} = \sum _l \alpha _l \mathbf {A}_l, \hspace{2.5pt} \mathbf {A}_l \in \mathcal {A}_\mathrm {MMV} \right\rbrace ,\) 
